Probability and “Anthropic” Arguments

The joke about this is that delays keep happening is because the LHD would
kill us all if it worked and that it’s anthropically likely that we’d be born
into a universe with a high population, one where human extinction keeps not
happening for “mysterious” reasons.

Here’s a selection from The Meaning of It All, an excellent book of a
set of three lectures by Richard Feynman:

I now turn to another kind of principle or idea, and that is that there is no
sense in calculating the probability or the chance that something happens
after it happens. A lot of scientists don’t even appreciate this. In fact,
the first time I got into an argument over this was when I was a graduate
student at Princeton, and there was a guy in the Psychology department who
was running rat races. I mean, he has a T-shaped thing, and the rats go, and
they go to the right, and the left, and so on. And it’s a general principle
of psychologists that in these tests they arrange so that the odds that the
things that happen happen by chance is small, in fact, less than one in
twenty. That means that one in twenty of their laws is probably wrong. But
the statistical ways of calculating the odds, like coin flipping if the rats
were to go randomly right and left, are easy to work out. This man had
designed and experiment which would show something which I do not remember,
if the rats always went to the right, let’s say. I can’t remember exactly. He
had to do a great number of tests, because, of course, they could go right
accidentally, so to get it down to one in twenty by odds, he had to do a
number of them. And it’s hard to do, and he did his number. Then he found
that it didn’t work. They went to the right, and they went to the left, and
so on. And then he noticed, most remarkably, that they alternated, first
right, then left, then right, then left. And then he ran to me, and he said,
“Calculate the probability for me that they should alternate, so that I can
see if it is less than one in twenty.” I said, “It probably is less than one
in twenty, but it doesn’t count.” He said, “Why?” I said, “Because it doesn’t
make any sense to calculate after the event. You see, you found the
peculiarity, and so you selected the peculiar case.”

For example, I had the most remarkable experience this evening. While coming
in here, I saw license plate ANZ 912. Calculate for me, please, the odds that
of all the license plates in the state of Washington I should happen to see
ANZ 912. Well, it’s a ridiculous thing. And, in the same way, what he must do
is this: The fact that the rat directions alternate suggests the possibility
that rats alternate. If he wants to test this hypothesis, one in twenty, he
cannot do it from the same data that gave him the clue. He must do another
experiment all over again and then see if they alternate. He did, and it
didn’t work.

The application of this principle to anthropic arguments is left as an
excercise for the reader.